## Abstract

Bounded local *G*-shtukas are function field analogs for *p*-divisible groups with extra structure. We describe their deformations and moduli spaces. The latter are analogous to Rapoport–Zink spaces for *p*-divisible groups. The underlying schemes of these moduli spaces are affine Deligne–Lusztig varieties. For basic Newton polygons the closed Newton stratum in the universal deformation of a local *G*-shtuka is isomorphic to the completion of a corresponding affine Deligne–Lusztig variety in that point. This yields bounds on the dimension and proves equidimensionality of the basic affine Deligne–Lusztig varieties.

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